Some have said a Turing machine is not realistic because it invokes
infinity, such as an infinitely long tape (memory), but this is not
true; it only needs a finite but indeterminate length of tape. Any
physical Turing machine would be running at a finite speed and so would
only need infinite tape if it were running for an infinite amount of
time. If I say I can prove this particular Turing machine will never
stop what I mean is that for any finite amount of time you give me I can
show you that if it still has enough (finite) tape then it is still
running.